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Mean-field dynamo theory has important applications in solar physics and galactic magnetism. We discuss some of the many turbulence effects relevant to the generation of large-scale magnetic fields in the solar convection zone. The mean-field description is then used to illustrate the physics of the α effect, turbulent pumping, turbulent magnetic diffusivity, and other effects on a modern solar dynamo model. We also discuss how turbulence transport coefficients are derived from local simulations of convection and then used in mean-field models. [ABSTRACT FROM AUTHOR]

The conversion of electromagnetic energy into magnetohydrodynamic energy occurs when the electric conductivity changes from negligible to finite values. This process is relevant during the epoch of reheating in the early universe at the end of inflation and before the emergence of the radiation-dominated era. We find that the conversion into kinetic and thermal energies is primarily the result of electric energy dissipation, while magnetic energy only plays a secondary role in this process. This means that since electric energy dominates over magnetic energy during inflation and reheating, significant amounts of electric energy can be converted into magnetohydrodynamic energy when conductivity emerges before the relevant length scales become stable. [ABSTRACT FROM AUTHOR]

Spiral galaxies, including the Milky Way, have large-scale magnetic fields with significant energy densities. The dominant theory attributes these magnetic fields to a large-scale dynamo. We review the current status of dynamo theory and discuss various numerical simulations designed either to explain particular aspects of the problem or to reproduce galactic magnetic fields globally. Our main conclusions can be summarized as follows: Idealized direct numerical simulations produce mean magnetic fields, whose saturation energy density tends to decline with increasing magnetic Reynolds number. This is still an unsolved problem. Large-scale galactic magnetic fields of microgauss strengths can probably be explained only if helical magnetic fields of small or moderate length scales can be rapidly ejected or destroyed. Small-scale dynamos are important throughout a galaxy's life and probably provide strong seed fields at early stages. The circumgalactic medium (CGM) may play an important role in driving dynamo action at small and large length scales. These interactions between the galactic disk and the CGM may provide important insights into our understanding of galactic dynamos. We expect future research in galactic dynamos to focus on the cosmological history of galaxies and the interaction with the CGM as means of replacing the idealized boundary conditions used in earlier work. [ABSTRACT FROM AUTHOR]

Magnetic helicity plays a tremendously important role when it is different from zero on average. Most notably, it leads to the phenomenon of an inverse cascade. Here, we consider decaying magnetohydrodynamic (MHD) turbulence as well as some less common examples of magnetic evolution under the Hall effect and ambipolar diffusion, as well as cases in which the magnetic field evolution is constrained by the presence of an asymmetry in the number density of chiral fermions, whose spin is systematically either aligned or anti-aligned with its momentum. In all those cases, there is a new conserved quantity: the Hosking integral. We present quantitative scaling results for the magnetic integral scale as well as the magnetic energy density and its spectrum. We also compare with cases were a magnetic version of the Saffman integral is initially finite. Rotation in MHD turbulence tends to suppress nonlinearity and thereby also inverse cascading. Finally, the role of the Hosking and magnetic Saffman integrals in shell models of turbulence is examined. [ABSTRACT FROM AUTHOR]

Small-scale dynamos play important roles in modern astrophysics, especially on galactic and extragalactic scales. Owing to dynamo action, purely hydrodynamic Kolmogorov turbulence hardly exists and is often replaced by hydromagnetic turbulence. Understanding the size of dissipative magnetic structures is important in estimating the time-scale of galactic scintillation and other observational and theoretical aspects of interstellar and intergalactic small-scale dynamos. Here we show that, during the kinematic phase of the small-scale dynamo, the cutoff wavenumber of the magnetic energy spectra scales as expected for large magnetic Prandtl numbers, but continues in the same way also for moderately small values – contrary to what is expected. For a critical magnetic Prandtl number of about 0.3, the dissipative and resistive cutoffs are found to occur at the same wavenumber. In the non-linearly saturated regime, the critical magnetic Prandtl number becomes unity. The cutoff scale now has a shallower scaling with magnetic Prandtl number below a value of about three, and a steeper one otherwise compared to the kinematic regime. [ABSTRACT FROM AUTHOR]

The magnetic fields in galaxy clusters and probably also in the interstellar medium are believed to be generated by a small-scale dynamo. Theoretically, during its kinematic stage, it is characterized by a Kazantsev spectrum, which peaks at the resistive scale. It is only slightly shallower than the Saffman spectrum that is expected for random and causally connected magnetic fields. Causally disconnected fields have the even steeper Batchelor spectrum. Here, we show that all three spectra are present in the small-scale dynamo. During the kinematic stage, the Batchelor spectrum occurs on scales larger than the energy-carrying scale of the turbulence, and the Kazantsev spectrum on smaller scales within the inertial range of the turbulence – even for a magnetic Prandtl number of unity. In the saturated state, the dynamo develops a Saffman spectrum on large scales, suggestive of the build-up of long-range correlations. At large magnetic Prandtl numbers, elongated structures are seen in synthetic synchrotron emission maps showing the parity-even E polarization. We also observe a significant excess in the E polarization over the parity-odd B polarization at subresistive scales, and a deficiency at larger scales. This finding is at odds with the observed excess in the Galactic microwave foreground emission, which is believed to be associated with larger scales. The E and B polarizations may be highly non-Gaussian and skewed in the kinematic regime of the dynamo. For dust emission, however, the polarized emission is always nearly Gaussian, and the excess in the E polarization is much weaker. [ABSTRACT FROM AUTHOR]

Spiral galaxies, including the Milky Way, have large-scale magnetic fields with significant energy densities. The dominant theory attributes these magnetic fields to a large-scale dynamo. We review the current status of dynamo theory and discuss various numerical simulations designed either to explain particular aspects of the problem or to reproduce galactic magnetic fields globally. Our main conclusions can be summarized as follows: Idealized direct numerical simulations produce mean magnetic fields, whose saturation energy density tends to decline with increasing magnetic Reynolds number. This is still an unsolved problem. Large-scale galactic magnetic fields of microgauss strengths can probably be explained only if helical magnetic fields of small or moderate length scales can be rapidly ejected or destroyed. Small-scale dynamos are important throughout a galaxy's life and probably provide strong seed fields at early stages. The circumgalactic medium (CGM) may play an important role in driving dynamo action at small and large length scales. These interactions between the galactic disk and the CGM may provide important insights into our understanding of galactic dynamos. We expect future research in galactic dynamos to focus on the cosmological history of galaxies and the interaction with the CGM as means of replacing the idealized boundary conditions used in earlier work. [ABSTRACT FROM AUTHOR]

In many astrophysical environments, self-gravity can generate kinetic energy, which, in principle, is available for driving dynamo action. Using direct numerical simulations, we show that in unstirred self-gravitating subsonic turbulence with helicity and a magnetic Prandtl number of unity, there is a critical magnetic Reynolds number of about 25 above which the work done against the Lorentz force exceeds the Ohmic dissipation. The collapse itself drives predominantly irrotational motions that cannot be responsible for dynamo action. We find that, with a weak magnetic field, one-third of the work done by the gravitational force goes into compressional heating and the remaining two-thirds go first into kinetic energy of the turbulence before a fraction of it is converted further into magnetic and finally thermal energies. Close to the collapse, however, these fractions change toward 1/4 and 3/4 for compressional heating and kinetic energy, respectively. When the magnetic field is strong, the compressional heating fraction is unchanged. Out of the remaining kinetic energy, one quarter goes directly into magnetic energy via work against the Lorentz force. The fraction of vortical motions diminishes in favour of compressive motions that are almost exclusively driven by the Jeans instability. For an initially uniform magnetic field, field amplification at scales larger than those of the initial turbulence are driven by tangling. [ABSTRACT FROM AUTHOR]

Radiation transport plays an important role in stellar atmospheres, but the effects of turbulence are being obscured by other effects such as stratification. Using radiative hydrodynamic simulations of forced turbulence, we determine the decay rates of sinusoidal large-scale temperature perturbations of different wavenumbers in the optically thick and thin regimes. Increasing the wavenumber increases the rate of decay in both regimes, but this effect is much weaker than for the usual turbulent diffusion of passive scalars, where the increase is quadratic for small wavenumbers. The turbulent decay is well described by an enhanced Newtonian cooling process in the optically thin limit, which is found to show a weak increase proportional to the square root of the wavenumber. In the optically thick limit, the increase in turbulent decay is somewhat steeper for wavenumbers below the energy-carrying wavenumber of the turbulence, but levels off toward larger wavenumbers. In the presence of turbulence, the typical cooling time is comparable to the turbulent turnover time. We observe that the temperature takes a long time to reach equilibrium in both the optically thin and thick cases, but in the former, the temperature retains smaller scale structures for longer. [ABSTRACT FROM AUTHOR]

We study the gravitational wave (GW) signal sourced by primordial turbulence that is assumed to be present at cosmological phase transitions like the electroweak and quantum chromodynamics phase transitions. We consider various models of primordial turbulence, such as those with and without helicity, purely hydrodynamical turbulence induced by fluid motions, and magnetohydrodynamic turbulence whose energy can be dominated either by kinetic or magnetic energy, depending on the nature of the turbulence. We also study circularly polarized GWs generated by parity violating sources such as helical turbulence. Our ultimate goal is to determine the efficiency of GW production through different classes of turbulence. We find that the GW energy and strain tend to be large for acoustic or irrotational turbulence, even though its tensor mode amplitude is relatively small at most wave numbers. Only at very small wave numbers is the spectral tensor mode significant, which might explain the efficient GW production in that case. [ABSTRACT FROM AUTHOR]

We discuss selected aspects regarding the magnetic field evolution of solar-type stars. Most of the stars with activity cycles are in the range where the normalized chromospheric Calcium emission increases linearly with the inverse Rossby number. For Rossby numbers below about a quarter of the solar value, the activity saturates and no cycles have been found. For Rossby numbers above the solar value, again no activity cycles have been found, but now the activity goes up again for a major fraction of the stars. Rapidly rotating stars show nonaxisymmetric large-scale magnetic fields, but there is disagreement between models and observations regarding the actual value of the Rossby number where this happens. We also discuss the prospects of detecting the sign of magnetic helicity using various linear polarization techniques both at the stellar surface using the parity-odd contribution to linear polarization and above the surface using Faraday rotation. [ABSTRACT FROM AUTHOR]

Relic gravitational waves (GWs) can be produced by primordial magnetic fields. However, not much is known about the resulting GW amplitudes and their dependence on the details of the generation mechanism. Here we treat magnetic field generation through the chiral magnetic effect (CME) as a generic mechanism and explore its dependence on the speed of generation (the product of magnetic diffusivity and characteristic wavenumber) and the speed characterizing the maximum magnetic field strength expected from the CME. When the latter exceeds the former (regime I), which is the regime applicable to the early universe, we obtain an inverse cascade with moderate GW energy that scales with the third power of the magnetic energy. When the generation speed exceeds the CME limit (regime II), the GW energy continues to increase without a corresponding increase of magnetic energy. In the early kinematic phase, the GW energy spectrum (per linear wavenumber interval) has opposite slopes in both regimes and is characterized by an inertial range spectrum in regime I and a white noise spectrum in regime II. The occurrence of these two slopes is shown to be a generic consequence of a nearly monochromatic exponential growth of the magnetic field. The resulting GW energy is found to be proportional to the fifth power of the limiting CME speed and the first power of the generation speed. [ABSTRACT FROM AUTHOR]

The ohmic decay of magnetic fields in the crusts of neutron stars is generally believed to be governed by Hall drift, which leads to what is known as a Hall cascade. Here we show that helical and fractionally helical magnetic fields undergo strong inverse cascading like in magnetohydrodynamics (MHD), but the magnetic energy decays more slowly with time t: instead of ∝t−2/3 in MHD. Even for a nonhelical magnetic field there is a certain degree of inverse cascading for sufficiently strong magnetic fields. The inertial range scaling with wavenumber k is compatible with earlier findings for the forced Hall cascade, i.e., proportional to k−7/3, but in the decaying cases, the subinertial range spectrum steepens to a novel k5 slope instead of the k4 slope in MHD. The energy of the large-scale magnetic field can increase quadratically in time through inverse cascading. For helical fields, the energy dissipation is found to be inversely proportional to the large-scale magnetic field and proportional to the fifth power of the rms magnetic field. For neutron star conditions with an rms magnetic field of a few times , the large-scale magnetic field might only be , while still producing magnetic dissipation of for thousands of years, which could manifest itself through X-ray emission. Finally, it is shown that the conclusions from local unstratified models agree rather well with those from stratified models with boundaries. [ABSTRACT FROM AUTHOR]

We study the prospects of detecting magnetic helicity in galaxies by observing the dust polarization of the edge-on galaxy NGC 891. Our numerical results of mean-field dynamo calculations show that there should be a large-scale component of the rotationally invariant parity-odd B polarization that we predict to be negative in the first and third quadrants, and positive in the second and fourth quadrants. The large-scale parity-even E polarization is predicted to be negative near the axis and positive further away in the outskirts. These properties are shown to be mostly a consequence of the magnetic field being azimuthal and the polarized intensity being maximum at the centre of the galaxy and are not a signature of magnetic helicity. [ABSTRACT FROM AUTHOR]

Explicit radiation hydrodynamic simulations of the atmospheres of massive stars and of convection in accretion discs around white dwarfs suffer from prohibitively short time steps due to radiation. This constraint is related to the cooling time rather than the radiative pressure, which also becomes important in hot stars and discs. We show that the radiative time step constraint is governed by the minimum of the sum of the optically thick and thin contributions rather than the smaller one of the two. In simulations with the Pencil Code, their weighting fractions are found empirically. In three-dimensional convective accretion disc simulations, the Deardorff term is found to be the main contributor to the enthalpy flux rather than the superadiabatic gradient. We conclude with a discussion of how the radiative time step problem could be mitigated in certain types of investigations. [ABSTRACT FROM AUTHOR]

Hydromagnetic turbulence produced during phase transitions in the early universe can be a powerful source of stochastic gravitational waves (GWs). GWs can be modelled by the linearised spatial part of the Einstein equations sourced by the Reynolds and Maxwell stresses. We have implemented two different GW solvers into the Pencil Code – a code which uses a third order timestep and sixth order finite differences. Using direct numerical integration of the GW equations, we study the appearance of a numerical degradation of the GW amplitude at the highest wavenumbers, which depends on the length of the timestep – even when the Courant–Friedrichs–Lewy condition is ten times below the stability limit. This degradation leads to a numerical error, which is found to scale with the third power of the timestep. A similar degradation is not seen in the magnetic and velocity fields. To mitigate numerical degradation effects, we alternatively use the exact solution of the GW equations under the assumption that the source is constant between subsequent timesteps. This allows us to use a much longer timestep, which cuts the computational cost by a factor of about ten. [ABSTRACT FROM AUTHOR]

In recent years, several optimal dynamos have been discovered. They minimize the magnetic energy dissipation or, equivalently, maximize the growth rate at a fixed magnetic Reynolds number. In the optimal dynamo of Willis (Phys. Rev. Lett., vol. 109, 2012, 251101), we find mean-field dynamo action for planar averages. One component of the magnetic field grows exponentially while the other decays in an oscillatory fashion near onset. This behaviour is different from that of an $\unicode[STIX]{x1D6FC}^{2}$ dynamo, where the two non-vanishing components of the planar averages are coupled and have the same growth rate. For the Willis dynamo, we find that the mean field is excited by a negative turbulent magnetic diffusivity, which has a non-uniform spatial profile near onset. The temporal oscillations in the decaying component are caused by the corresponding component of the diffusivity tensor being complex when the mean field is decaying and, in this way, time dependent. The growing mean field can be modelled by a negative magnetic diffusivity combined with a positive magnetic hyperdiffusivity. In two other classes of optimal dynamos of Chen et al. (J. Fluid Mech., vol. 783, 2015, pp. 23–45), we find, to some extent, similar mean-field dynamo actions. When the magnetic boundary conditions are mixed, the two components of the planar averaged field grow at different rates when the dynamo is 15 % supercritical. When the mean magnetic field satisfies homogeneous boundary conditions (where the magnetic field is tangential to the boundary), mean-field dynamo action is found for one-dimensional averages, but not for planar averages. Despite having different spatial profiles, both dynamos show negative turbulent magnetic diffusivities. Our finding suggests that negative turbulent magnetic diffusivities may support a broader class of dynamos than previously thought, including these three optimal dynamos. [ABSTRACT FROM AUTHOR]

We investigate the effect of turbulence on the combined condensational and collisional growth of cloud droplets by means of high-resolution direct numerical simulations of turbulence and a superparticle approximation for droplet dynamics and collisions. The droplets are subject to turbulence as well as gravity, and their collision and coalescence efficiencies are taken to be unity. We solve the thermodynamic equations governing temperature, water vapor mixing ratio, and the resulting supersaturation fields together with the Navier–Stokes equation. We find that the droplet size distribution broadens with increasing Reynolds number and/or mean energy dissipation rate. Turbulence affects the condensational growth directly through supersaturation fluctuations, and it influences collisional growth indirectly through condensation. Our simulations show for the first time that, in the absence of the mean updraft cooling, supersaturation-fluctuation-induced broadening of droplet size distributions enhances the collisional growth. This is contrary to classical (nonturbulent) condensational growth, which leads to a growing mean droplet size, but a narrower droplet size distribution. Our findings, instead, show that condensational growth facilitates collisional growth by broadening the size distribution in the tails at an early stage of rain formation. With increasing Reynolds numbers, evaporation becomes stronger. This counteracts the broadening effect due to condensation at late stages of rain formation. Our conclusions are consistent with results of laboratory experiments and field observations, and show that supersaturation fluctuations are important for precipitation. [ABSTRACT FROM AUTHOR]

We study the effects of ambipolar diffusion (AD) on hydromagnetic turbulence. We consider the regime of large magnetic Prandtl number, relevant to the interstellar medium. In most of the cases, we use the single-fluid approximation where the drift velocity between charged and neutral particles is proportional to the Lorentz force. In two cases we also compare with the corresponding two-fluid model, where ionization and recombination are included in the continuity and momentum equations for the neutral and charged species. The magnetic field properties are found to be well represented by the single-fluid approximation. We quantify the effects of AD on total and spectral kinetic and magnetic energies, the ohmic and AD dissipation rates, the statistics of the magnetic field, the current density, and the linear polarization as measured by the rotationally invariant E and B mode polarizations. We show that the kurtosis of the magnetic field decreases with increasing AD. The E mode polarization changes its skewness from positive values for small AD to negative ones for large AD. Even when AD is weak, changes in AD have a marked effect on the skewness and kurtosis of E , and only a weak effect on those of B. These results open the possibility of employing E and B mode polarizations as diagnostic tools for characterizing turbulent properties of the interstellar medium. [ABSTRACT FROM AUTHOR]

We investigate the effect of turbulence on the collisional growth of micrometer-sized droplets through high-resolution numerical simulations with well-resolved Kolmogorov scales, assuming a collision and coalescence efficiency of unity. The droplet dynamics and collisions are approximated using a superparticle approach. In the absence of gravity, we show that the time evolution of the shape of the droplet-size distribution due to turbulence-induced collisions depends strongly on the turbulent energy-dissipation rate , but only weakly on the Reynolds number. This can be explained through the dependence of the mean collision rate described by the Saffman–Turner collision model. Consistent with the Saffman–Turner collision model and its extensions, the collision rate increases as even when coalescence is invoked. The size distribution exhibits power-law behavior with a slope of −3.7 from a maximum at approximately 10 up to about 40 μm. When gravity is invoked, turbulence is found to dominate the time evolution of an initially monodisperse droplet distribution at early times. At later times, however, gravity takes over and dominates the collisional growth. We find that the formation of large droplets is very sensitive to the turbulent energy dissipation rate. This is because turbulence enhances the collisional growth between similar-sized droplets at the early stage of raindrop formation. The mean collision rate grows exponentially, which is consistent with the theoretical prediction of the continuous collisional growth even when turbulence-generated collisions are invoked. This consistency only reflects the mean effect of turbulence on collisional growth. [ABSTRACT FROM AUTHOR]

To explain the large‐scale magnetic field of the sun and other bodies, the mean‐field dynamo theory is commonly applied, where one solves the averaged equations for the mean magnetic field. However, the standard approach breaks down when the scale of the turbulent eddies becomes comparable to the scale of the variations of the mean magnetic field. Models showing sharp magnetic field structures have therefore been regarded as unreliable. Our aim is to look for new effects that occur when we relax the restrictions of the standard approach, which becomes particularly important at the bottom of the convection zone where the size of the turbulent eddies is comparable to the depth of the convection zone itself. We approximate the underlying integro‐differential equation using a partial differential equation corresponding to a reaction–diffusion‐type equation for the mean electromotive force, making an approach that is nonlocal in space and time feasible under conditions where spherical geometry and nonlinearity are included. In agreement with earlier findings, spatiotemporal nonlocality lowers the excitation conditions of the dynamo. Sharp structures are now found to be absent. However, in the surface layers, the field remains similar to before. [ABSTRACT FROM AUTHOR]

Recent direct numerical simulations (DNS) of large-scale turbulent dynamos in strongly stratified layers have resulted in surprisingly sharp bipolar structures at the surface. Here, we present new DNS of helically and non-helically forced turbulence with and without rotation and compare with corresponding mean-field simulations (MFS) to show that these structures are a generic outcome of a broader class of dynamos in density-stratified layers. The MFS agree qualitatively with the DNS, but the period of oscillations tends to be longer in the DNS. In both DNS and MFS, the sharp structures are produced by converging flows at the surface and might be driven in non-linear stage of evolution by the Lorentz force associated with the large-scale dynamo-driven magnetic field if the dynamo number is at least 2.5 times supercritical. [ABSTRACT FROM AUTHOR]

In the presence of magnetic helicity, inverse transfer from small to large scales is well known in magnetohydrodynamic (MHD) turbulence and has applications in astrophysics, cosmology, and fusion plasmas. Using high resolution direct numerical simulations of magnetically dominated self-similarly decaying MHD turbulence, we report a similar inverse transfer even in the absence of magnetic helicity. We compute for the first time spectral energy transfer rates to show that this inverse transfer is about half as strong as with helicity, but in both cases the magnetic gain at large scales results from velocity at similar scales interacting with smaller-scale magnetic fields. This suggests that both inverse transfers are a consequence of universal mechanisms for magnetically dominated turbulence. Possible explanations include inverse cascading of the mean squared vector potential associated with local near two dimensionality and the shallower k2 subinertial range spectrum of kinetic energy forcing the magnetic field with a k4 subinertial range to attain larger-scale coherence. The inertial range shows a clear k-2 spectrum and is the first example of fully isotropic magnetically dominated MHD turbulence exhibiting weak turbulence scaling. [ABSTRACT FROM AUTHOR]

With the ultimate aim of using the fundamental or f mode to study helioseismic aspects of turbulence-generated magnetic flux concentrations, we use randomly forced hydromagnetic simulations of a piecewise isothermal layer in two dimensions with reflecting boundaries at top and bottom. We compute numerically diagnostic wavenumber–frequency diagrams of the vertical velocity at the interface between the denser gas below and the less dense gas above. For an Alfvén-to-sound speed ratio of about 0.1, a 5 per cent frequency increase of the f mode can be measured when kxHp = 3–4, where kx is the horizontal wavenumber and Hp is the pressure scaleheight at the surface. Since the solar radius is about 2000 times larger than Hp, the corresponding spherical harmonic degree would be 6000–8000. For weaker fields, a kx-dependent frequency decrease by the turbulent motions becomes dominant. For vertical magnetic fields, the frequency is enhanced for kxHp ≈ 4, but decreased relative to its nonmagnetic value for kxHp ≈ 9. [ABSTRACT FROM AUTHOR]

Using direct numerical simulations (DNS), we verify that in the kinematic regime, a turbulent helical dynamo grows in such a way that the magnetic energy spectrum remains to high-precision shape-invariant, i.e. at each wavenumber k the spectrum grows with the same growth rate. Signatures of large-scale dynamo action can be identified through the excess of magnetic energy at small k, of one of the two oppositely polarized constituents. Also a suitably defined planar average of the magnetic field can be chosen such that its rms value isolates the strength of the mean field. However, these different means of analysis suggest that the strength of the large-scale field diminishes with increasing magnetic Reynolds number ReM like ${\rm Re}_{\rm M}^{-1/2}$ for intermediate values and like ${\rm Re}_{\rm M}^{-3/4}$ for larger ones. Both an analysis from the Kazantsev model including helicity and the DNS show that this arises due to the magnetic energy spectrum still peaking at resistive scales, even when helicity is present. As expected, the amplitude of the large-scale field increases with increasing fractional helicity, enabling us to determine the onset of large-scale dynamo action and distinguishing it from that of the small-scale dynamo. Our DNS show that, contrary to earlier results for smaller scale separation (only 1.5 instead of now 4), the small-scale dynamo can still be excited at magnetic Prandtl numbers of 0.1 and only moderate values of the magnetic Reynolds numbers (∼160). [ABSTRACT FROM AUTHOR]

Using one-dimensional models, we show that a helical magnetic field with an appropriate sign of helicity can compensate the Faraday depolarization resulting from the superposition of Faraday-rotated polarization planes from a spatially extended source. For radio emission from a helical magnetic field, the polarization as a function of the square of the wavelength becomes asymmetric with respect to zero. Mathematically speaking, the resulting emission occurs then either at observable or at unobservable (imaginary) wavelengths. We demonstrate that rotation measure (RM) synthesis allows for the reconstruction of the underlying Faraday dispersion function in the former case, but not in the latter. The presence of positive magnetic helicity can thus be detected by observing positive RM in highly polarized regions in the sky and negative RM in weakly polarized regions. Conversely, negative magnetic helicity can be detected by observing negative RM in highly polarized regions and positive RM in weakly polarized regions. The simultaneous presence of two magnetic constituents with opposite signs of helicity is shown to possess signatures that can be quantified through polarization peaks at specific wavelengths and the gradient of the phase of the Faraday dispersion function. Similar polarization peaks can tentatively also be identified for the bi-helical magnetic fields that are generated self-consistently by a dynamo from helically forced turbulence, even though the magnetic energy spectrum is then continuous. Finally, we discuss the possibility of detecting magnetic fields with helical and non-helical properties in external galaxies using the Square Kilometre Array. [ABSTRACT FROM AUTHOR]

We solve for the motion of charged particles in a helical time-periodic ABC (Arnold-Beltrami-Childress) magnetic field. The magnetic field lines of a stationary ABC field with coefficients A = B = C = 1 are chaotic, and we show that the motion of a charged particle in such a field is also chaotic at late times with positive Lyapunov exponent. We further show that in time-periodic ABC fields, the kinetic energy of a charged particle can increase indefinitely with time. At late times the mean kinetic energy grows as a power law in time with an exponent that approaches unity. For an initial distribution of particles, whose kinetic energy is uniformly distributed within some interval, the probability density function of kinetic energy is, at late times, close to a Gaussian but with steeper tails. [ABSTRACT FROM AUTHOR]

The negative effective magnetic-pressure instability operates on scales encompassing many turbulent eddies, which correspond to convection cells in the Sun. This instability is discussed here in connection with the formation of active regions near the surface layers of the Sun. This instability is related to the negative contribution of turbulence to the mean magnetic pressure that causes the formation of large-scale magnetic structures. For an isothermal layer, direct numerical simulations and mean-field simulations of this phenomenon are shown to agree in many details, for example the onset of the instability occurs at the same depth. This depth increases with increasing field strength, such that the growth rate of this instability is independent of the field strength, provided the magnetic structures are fully contained within the domain. A linear stability analysis is shown to support this finding. The instability also leads to a redistribution of turbulent intensity and gas pressure that could provide direct observational signatures. [ABSTRACT FROM AUTHOR]

Magnetic field generation on scales that are large compared with the scale of the turbulent eddies is known to be possible via the so-called a effect when the turbulence is helical and if the domain is large enough for the a effect to dominate over turbulent diffusion. Using three-dimensional turbulence simulations, we show that the energy of the resulting mean magnetic field of the saturated state increases linearly with the product of normalized helicity and the ratio of domain scale to eddy scale, provided this product exceeds a critical value of around unity. This implies that large-scale dynamo action commences when the normalized helicity is larger than the inverse scale ratio. Our results show that the emergence of small-scale dynamo action does not have any noticeable effect on the large-scale dynamo. Recent findings by Pietarila Graham et al. [Phys. Rev. E 85, 066406 (2012)] of a smaller minimal helicity may be an artifact due to the onset of small-scale dynamo action at large magnetic Reynolds numbers. However, the onset of large-scale dynamo action is difficult to establish when the kinetic helicity is small. Instead of random forcing, they used an ABC flow with time-dependent phases. We show that such dynamos saturate prematurely in a way that is reminiscent of inhomogeneous dynamos with internal magnetic helicity fluxes. Furthermore, even for very low fractional helicities, such dynamos display large-scale fields that change direction, which is uncharacteristic of turbulent dynamos. [ABSTRACT FROM AUTHOR]

The negative effective magnetic pressure instability discovered recently in direct numerical simulations (DNSs) may play a crucial role in the formation of sunspots and active regions in the Sun and stars. This instability is caused by a negative contribution of turbulence to the effective mean Lorentz force (the sum of turbulent and non-turbulent contributions) and results in the formation of large-scale inhomogeneous magnetic structures from an initially uniform magnetic field. Earlier investigations of this instability in DNSs of stably stratified, externally forced, isothermal hydromagnetic turbulence in the regime of large plasma β are now extended into the regime of larger scale separation ratios where the number of turbulent eddies in the computational domain is about 30. Strong spontaneous formation of large-scale magnetic structures is seen even without performing any spatial averaging. These structures encompass many turbulent eddies. The characteristic time of the instability is comparable to the turbulent diffusion time, L/ η, where η is the turbulent diffusivity and L is the scale of the domain. DNSs are used to confirm that the effective magnetic pressure does indeed become negative for magnetic field strengths below the equipartition field. The dependence of the effective magnetic pressure on the field strength is characterized by fit parameters that seem to show convergence for larger values of the magnetic Reynolds number. [ABSTRACT FROM AUTHOR]

Several recent advances in turbulent dynamo theory are reviewed. High resolution simulations of small-scale and large-scale dynamo action in periodic domains are compared with each other and contrasted with similar results at low magnetic Prandtl numbers. It is argued that all the different cases show similarities at intermediate length scales. On the other hand, in the presence of helicity of the turbulence, power develops on large scales, which is not present in non-helical small-scale turbulent dynamos. At small length scales, differences occur in connection with the dissipation cutoff scales associated with the respective value of the magnetic Prandtl number. These differences are found to be independent of whether or not there is large-scale dynamo action. However, large-scale dynamos in homogeneous systems are shown to suffer from resistive slow-down even at intermediate length scales. The results from simulations are connected to mean field theory and its applications. Recent work on magnetic helicity fluxes to alleviate large-scale dynamo quenching, shear dynamos, nonlocal effects and magnetic structures from strong density stratification are highlighted. Several insights which arise from analytic considerations of small-scale dynamos are discussed. [ABSTRACT FROM AUTHOR]

We study spontaneous breakdown of chiral symmetry during the nonlinear evolution of the Tayler instability. We start with an initial steady state of zero helicity. Within linearized perturbation calculations, helical perturbations of this initial state have the same growth rate for either sign of helicity. Direct numerical simulations (DNS) of the fully nonlinear equations, however, show that an infinitesimal excess of one sign of helicity in the initial perturbation gives rise to a saturated helical state. We further show that this symmetry breaking can be described by weakly nonlinear finite-amplitude equations with undetermined coefficients which can be deduced solely from symmetry consideration. By fitting solutions of the amplitude equations to data from DNS, we further determine the coefficients of the amplitude equations. [ABSTRACT FROM AUTHOR]

To understand the basic mechanism of the formation of magnetic flux concentrations, we determine by direct numerical simulations the turbulence contributions to the mean magnetic pressure in a strongly stratified isothermal layer with large plasma beta, where a weak uniform horizontal mean magnetic field is applied. The negative contribution of turbulence to the effective mean magnetic pressure is determined for strongly stratified forced turbulence over a range of values of magnetic Reynolds and Prandtl numbers. Small-scale dynamo action is shown to reduce the negative effect of turbulence on the effective mean magnetic pressure. However, the turbulence coefficients describing the negative effective magnetic pressure phenomenon are found to converge for magnetic Reynolds numbers between 60 and 600, which is the largest value considered here. In all these models, the turbulent intensity is arranged to be nearly independent of height, so the kinetic energy density decreases with height due to the decrease in density. In a second series of numerical experiments, the turbulent intensity increases with height such that the turbulent kinetic energy density is nearly independent of height. Turbulent magnetic diffusivity and turbulent pumping velocity are determined with the test-field method for both cases. The vertical profile of the turbulent magnetic diffusivity is found to agree with what is expected based on simple mixing length expressions. Turbulent pumping is shown to be down the gradient of turbulent magnetic diffusivity, but it is twice as large as expected. Corresponding numerical mean-field models are used to show that a large-scale instability can occur in both cases, provided the degree of scale separation is large enough and hence the turbulent magnetic diffusivity small enough. [ABSTRACT FROM AUTHOR]

ABSTRACT We consider mean-field dynamo models with fluctuating α effect, both with and without large-scale shear. The α effect is chosen to be Gaussian white noise with zero mean and a given covariance. In the presence of shear, we show analytically that (in infinitely large domains) the mean-squared magnetic field shows exponential growth. The growth rate of the fastest growing mode is proportional to the shear rate. This result agrees with earlier numerical results of Yousef et al. and the recent analytical treatment by Heinemann, McWilliams & Schekochihin who use a method different from ours. In the absence of shear, an incoherent α2 dynamo may also be possible. We further show by explicit calculation of the growth rate of third- and fourth-order moments of the magnetic field that the probability density function of the mean magnetic field generated by this dynamo is non-Gaussian. [ABSTRACT FROM AUTHOR]

Using mean-field theory, we compute the evolution of the magnetic field in a cylinder with outer perfectly conducting boundaries and imposed axial magnetic and electric fields. The thus injected magnetic helicity in the system can be redistributed by magnetic helicity fluxes down the gradient of the local current helicity of the small-scale magnetic field. A weak reversal of the axial magnetic field is found to be a consequence of the magnetic helicity flux in the system. Such fluxes are known to alleviate so-called catastrophic quenching of the α effect in astrophysical applications. A stronger field reversal can be obtained if there is also a significant kinetic α effect. Application to the reversed field pinch in plasma confinement devices is discussed. [ABSTRACT FROM AUTHOR]

Saturated small-scale dynamo solutions driven by isotropic non-helical turbulence are presented at low magnetic Prandtl numbers PrM down to 0.01. For PrM < 0.1, most of the energy is dissipated via Joule heat and, in agreement with earlier results for helical large-scale dynamos, kinetic energy dissipation is shown to diminish proportional to Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed. down to values of 0.1. In agreement with earlier work, there is, in addition to a short Golitsyn k-11/3 spectrum near the resistive scale, also some evidence for a short k-1 spectrum on larger scales. The rms magnetic field strength of the small-scale dynamo is found to depend only weakly on the value of PrM and decreases by about a factor of two as PrM is decreased from 1 to 0.01. The possibility of dynamo action at PrM = 0.1 in the nonlinear regime is argued to be a consequence of a suppression of the bottleneck seen in the kinetic energy spectrum in the absence of a dynamo and, more generally, a suppression of kinetic energy near the dissipation wavenumber. [ABSTRACT FROM AUTHOR]

Certain aspects of the mean-field theory of turbulent passive scalar transport and of mean-field electrodynamics are considered with particular emphasis on aspects of compressible fluids. It is demonstrated that the total mean-field diffusivity for passive scalar transport in a compressible flow may well be smaller than the molecular diffusivity. This is in full analogy to an old finding regarding the magnetic mean-field diffusivity in an electrically conducting turbulently moving compressible fluid. These phenomena occur if the irrotational part of the motion dominates the vortical part, the Péclet or magnetic Reynolds number is not too large, and, in addition, the variation of the flow pattern is slow. For both the passive scalar and the magnetic cases several further analytical results on mean-field diffusivities and related quantities found within the second-order correlation approximation are presented, as well as numerical results obtained by the test-field method, which applies independently of this approximation. Particular attention is paid to nonlocal and noninstantaneous connections between the turbulence-caused terms and the mean fields. Two examples of irrotational flows, in which interesting phenomena in the above sense occur, are investigated in detail. In particular, it is demonstrated that the decay of a mean scalar in a compressible fluid under the influence of these flows can be much slower than without any flow, and can be strongly influenced by the so-called memory effect, that is, the fact that the relevant mean-field coefficients depend on the decay rates themselves. [ABSTRACT FROM AUTHOR]

Autocatalysis is a fundamental concept, used in a wide range of domains. From the most general definition of autocatalysis, that is, a process in which a chemical compound is able to catalyze its own formation, several different systems can be described. We detail the different categories of autocatalyses and compare them on the basis of their mechanistic, kinetic, and dynamic properties. It is shown how autocatalytic patterns can be generated by different systems of chemical reactions. With the notion of autocatalysis covering a large variety of mechanistic Realizations with very similar behaviors, it is proposed that the key signature of autocatalysis is its kinetic pattern expressed in a mathematical form. [ABSTRACT FROM AUTHOR]

We present calculations of the relaxation of magnetic field structures that have the shape of particular knots and links. A set of helical magnetic flux configurations is considered, which we call n-foil knots of which the trefoil knot is the most primitive member. We also consider two nonhelical knots; namely, the Borromean rings as well as a single interlocked flux rope that also serves as the logo of the Inter-University Centre for Astronomy and Astrophysics in Pune, India. The field decay characteristics of both configurations is investigated and compared with previous calculations of helical and nonhelical triple-ring configurations. Unlike earlier nonhelical configurations, the present ones cannot trivially be reduced via flux annihilation to a single ring. For the n-foil knots the decay is described by power laws that range form t-2/3 to t-1/3, which can be as slow as the t-1/3 behavior for helical triple-ring structures that were seen in earlier work. The two nonhelical configurations decay like t-1, which is somewhat slower than the previously obtained t-3/2 behavior in the decay of interlocked rings with zero magnetic helicity. We attribute the difference to the creation of local structures that contain magnetic helicity which inhibits the field decay due to the existence of a lower bound imposed by the realizability condition. We show that net magnetic helicity can be produced resistively as a result of a slight imbalance between mutually canceling helical pieces as they are being driven apart. We speculate that higher order topological invariants beyond magnetic helicity may also be responsible for slowing down the decay of the two more complicated nonhelical structures mentioned above. [ABSTRACT FROM AUTHOR]

Some of the contributions of Chandrasekhar to the field of magnetohydrodynamics are highlighted. Particular emphasis is placed on the Chandrasekhar-Kendall functions that allow a decomposition of a vector field into right- and left-handed contributions. Magnetic energy spectra of both contributions are shown for a new set of helically forced simulations at resolutions higher than what has been available so far. For a forcing function with positive helicity, these simulations show a forward cascade of the right-handed contributions to the magnetic field and nonlocal inverse transfer for the left-handed contributions. The speed of inverse transfer is shown to decrease with increasing value of the magnetic Reynolds number. [ABSTRACT FROM AUTHOR]

We determine the magnetic helicity, along with the magnetic energy, at high latitudes using data from the Ulysses mission. The data set spans the time period from 1993 to 1996. The basic assumption of the analysis is that the solar wind is homogeneous. Because the solar wind speed is high, we follow the approach first pioneered by Matthaeus et al. by which, under the assumption of spatial homogeneity, one can use Fourier transforms of the magnetic field time series to construct one-dimensional spectra of the magnetic energy and magnetic helicity under the assumption that the Taylor frozen-in-flow hypothesis is valid. That is a well-satisfied assumption for the data used in this study. The magnetic helicity derives from the skew-symmetric terms of the three-dimensional magnetic correlation tensor, while the symmetric terms of the tensor are used to determine the magnetic energy spectrum. Our results show a sign change of magnetic helicity at wavenumber k ≈ 2 AU-1 (or frequency v ≈ 2 μHz) at distances below 2.8 AU and at k ≈ 30 AU-1 (or v ≈ 25 μHz) at larger distances. At small scales the magnetic helicity is positive at northern heliographic latitudes and negative at southern latitudes. The positive magnetic helicity at small scales is argued to be the result of turbulent diffusion reversing the sign relative to what is seen at small scales at the solar surface. Furthermore, the magnetic helicity declines toward solar minimum in 1996. The magnetic helicity flux integrated separately over one hemisphere amounts to about 1045 Mx2 cycle-1 at large scales and to a three times lower value at smaller scales. [ABSTRACT FROM AUTHOR]

Autocatalysis is a fundamental concept, used in a wide range of domains. From its most general definition, that is, a process in which a chemical compound is able to catalyze its own formation, several different systems can be described. We detail the different categories of autocatalyses, and compare them on the basis of their mechanistic, kinetic, and dynamic properties. It is shown how autocatalytic patterns can be generated by different systems of chemical reactions. The notion of autocatalysis covers a large variety of mechanistic realizations with very similar behaviors; it is proposed that its key signature is its kinetic pattern expressed in a mathematical form. This notion, while describing dynamic behaviors at the most fundamental level, is at the basis for developing higher-level concepts towards life: autocatalytic sets and autopoietic systems. [ABSTRACT FROM AUTHOR]

Direct numerical simulations and mean-field theory are used to model reactive front propagation in a turbulent medium. In the mean-field approach, memory effects of turbulent diffusion are taken into account to estimate the front speed in cases in which the Damköhler number is large. This effect is found to saturate the front speed to values comparable with the speed of the turbulent motions. By comparing with direct numerical simulations, it is found that the effective correlation time is much shorter than for nonreacting flows. The nonlinearity of the reaction term is found to make the front speed slightly faster. [ABSTRACT FROM AUTHOR]

We present the results of simulations of forced turbulence in a slab where the mean kinetic helicity has a maximum near the mid-plane, generating gradients of magnetic helicity of both large and small-scale fields. We also study systems that have poorly conducting buffer zones away from the midplane in order to assess the effects of boundaries. The dynamical α quenching phenomenology requires that the magnetic helicity in the small-scale fields approaches a nearly static, gauge independent state. To stress-test this steady state condition we choose a system with a uniform sign of kinetic helicity, so that the total magnetic helicity can reach a steady state value only through fluxes through the boundary, which are themselves suppressed by the velocity boundary conditions. Even with such a set up, the small-scale magnetic helicity is found to reach a steady state. In agreement with the earlier work, the magnetic helicity fluxes of small-scale fields are found to be turbulently diffusive. By comparing results with and without halos, we show that artificial constraints on magnetic helicity at the boundary do not have a significant impact on the evolution of the magnetic helicity, except that 'softer' (halo) boundary conditions give a lower energy of the saturated mean magnetic field. [ABSTRACT FROM AUTHOR]

The small-scale magnetic helicity produced as a by-product of the large-scale dynamo is believed to play a major role in dynamo saturation. In a mean-field model the generation of small-scale magnetic helicity can be modelled by using the dynamical quenching formalism. Catastrophic quenching refers to a decrease of the saturation field strength with increasing Reynolds number. It has been suggested that catastrophic quenching only affects the region of non-zero helical turbulence (i.e. where the kinematic α operates) and that it is possible to alleviate catastrophic quenching by separating the region of strong shear from the α layer. We perform a systematic study of a simple axisymmetric two-layer αΩ dynamo in a spherical shell for Reynolds numbers in the range 1 ≤ Rm ≤ 105. In the framework of dynamical quenching we show that this may not be the case, suggesting that magnetic helicity fluxes would be necessary. [ABSTRACT FROM AUTHOR]

Using two- and three-dimensional hydromagnetic simulations for a range of different flows, including laminar and turbulent ones, it is shown that solutions expressing the field in terms of Euler potentials (EP) are in general incorrect if the EP are evolved with an artificial diffusion term. In three dimensions, standard methods using the magnetic vector potential are found to permit dynamo action when the EP give decaying solutions. With an imposed field, the EP method yields excessive power at small scales. This effect is more exaggerated in the dynamic case, suggesting an unrealistically reduced feedback from the Lorentz force. The EP approach agrees with standard methods only at early times when magnetic diffusivity did not have time to act. It is demonstrated that the usage of EP with even a small artificial magnetic diffusivity does not converge to a proper solution of hydromagnetic turbulence. The source of this disagreement is not connected with magnetic helicity or the three-dimensionality of the magnetic field, but is simply due to the fact that the non-linear representation of the magnetic field in terms of EP that depend on the same coordinates is incompatible with the linear diffusion operator in the induction equation. [ABSTRACT FROM AUTHOR]

The generation of mean magnetic fields is studied for a simple non-helical flow where a net cross-helicity of either sign can emerge. This flow, which is also known as the Archontis flow, is a generalization of the Arnold–Beltrami–Childress flow, but with the cosine terms omitted. The presence of cross-helicity leads to a mean-field dynamo effect that is known as the Yoshizawa effect. Direct numerical simulations of such flows demonstrate the presence of magnetic fields on scales larger than the scale of the flow. Contrary to earlier expectations, the Yoshizawa effect is found to be proportional to the mean magnetic field and can therefore lead to its exponential instead of just linear amplification for magnetic Reynolds numbers that exceed a certain critical value. Unlike α effect dynamos, it is found that the Yoshizawa effect is not notably constrained by the presence of a conservation law. It is argued that this is due to the presence of a forcing term in the momentum equation, which leads to a non-zero correlation with the magnetic field. Finally, the application to energy convergence in solar wind turbulence is discussed. [ABSTRACT FROM AUTHOR]

Using mean-field models with a dynamical quenching formalism, we show that in finite domains magnetic helicity fluxes associated with small-scale magnetic fields are able to alleviate catastrophic quenching. We consider fluxes that result from advection by a mean flow, the turbulent mixing down the gradient of mean small-scale magnetic helicity density or the explicit removal which may be associated with the effects of coronal mass ejections in the Sun. In the absence of shear, all the small-scale magnetic helicity fluxes are found to be equally strong for both large- and small-scale fields. In the presence of shear, there is also an additional magnetic helicity flux associated with the mean field, but this flux does not alleviate catastrophic quenching. Outside the dynamo-active region, there are neither sources nor sinks of magnetic helicity, so in a steady state this flux must be constant. It is shown that unphysical behaviour emerges if the small-scale magnetic helicity flux is forced to vanish within the computational domain. [ABSTRACT FROM AUTHOR]